What is the derivative of a+bx+cx^2+dx^3 ?

The derivative of a+bx+cx^2+dx^3 is 3dx^2+2cx+b

What is the first derivative of a+bx+cx^2+dx^3 ?

The first derivative of a+bx+cx^2+dx^3 is 3dx^2+2cx+b

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\frac{d}{d x} (a + b x + c x^{2} + d x^{3})

3 d x^{2} + 2 c x + b

Solution steps

\frac{d}{d x} (a + b x + c x^{2} + d x^{3})

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d a}{d x} + \frac{d}{d x} (b x) + \frac{d}{d x} (c x^{2}) + \frac{d}{d x} (d x^{3})

\frac{d a}{d x} = 0

\frac{d}{d x} (b x) = b

\frac{d}{d x} (c x^{2}) = 2 c x

\frac{d}{d x} (d x^{3}) = 3 d x^{2}

= 0 + b + 2 c x + 3 d x^{2}

Simplify

= 3 d x^{2} + 2 c x + b

What is the derivative of a+bx+cx^2+dx^3 ?
The derivative of a+bx+cx^2+dx^3 is 3dx^2+2cx+b
What is the first derivative of a+bx+cx^2+dx^3 ?
The first derivative of a+bx+cx^2+dx^3 is 3dx^2+2cx+b